Game downloads on PS4 have a reputation of being very slow, with many people reporting downloads being an order of magnitude faster on Steam or Xbox. This had long been on my list of things to look into, but at a pretty low priority. After all, the PS4 operating system is based on a reasonably modern FreeBSD (9.0), so there should not be any crippling issues in the TCP stack. The implication is that the problem is something boring, like an inadequately dimensioned CDN.

The PS3 had a similar issue, which was fixed by a local proxy. Probably why I haven't really noticed on the PS4.

The problem isn't when you get a new game (yeah I had to leave mine on all night for Horizon: Zero Dawn as well). But when you're playing a game like Lego Dimensions and you can't play a new expansion right away because it starts downloading as soon as you place the character on the dimension pad.